Name: Symmetrization in Analysis (New Mathematical Monographs) (en Inglés)
Price: 245.60 USD
Availability: InStock
Author: Albert Baernstein Ii
ISBN: 9780521830478

portada Symmetrization in Analysis (New Mathematical Monographs) (en Inglés)

Symmetrization in Analysis (New Mathematical Monographs) (en Inglés)

Formato

Libro Físico

Editorial

Cambridge University Press

Autor

Albert Baernstein Ii

Año

2019

Idioma

Inglés

N° páginas

490

Encuadernación

Tapa Dura

ISBN

0521830478

ISBN13

9780521830478

N° edición

Categorías

Álgebra

Symmetrization in Analysis (New Mathematical Monographs) (en Inglés)

Albert Baernstein Ii (Autor) · Cambridge University Press · Tapa Dura

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Reseña del libro "Symmetrization in Analysis (New Mathematical Monographs) (en Inglés)"

Symmetrization is a rich area of mathematical analysis whose history reaches back to antiquity. This book presents many aspects of the theory, including symmetric decreasing rearrangement and circular and Steiner symmetrization in Euclidean spaces, spheres and hyperbolic spaces. Many energies, frequencies, capacities, eigenvalues, perimeters and function norms are shown to either decrease or increase under symmetrization. The book begins by focusing on Euclidean space, building up from two-point polarization with respect to hyperplanes. Background material in geometric measure theory and analysis is carefully developed, yielding self-contained proofs of all the major theorems. This leads to the analysis of functions defined on spheres and hyperbolic spaces, and then to convolutions, multiple integrals and hypercontractivity of the Poisson semigroup. The author's 'star function' method, which preserves subharmonicity, is developed with applications to semilinear PDEs. The book concludes with a thorough self-contained account of the star function's role in complex analysis, covering value distribution theory, conformal mapping and the hyperbolic metric.